U.S. patent number 4,978,920 [Application Number 07/338,392] was granted by the patent office on 1990-12-18 for magnetic field screens.
This patent grant is currently assigned to National Research Development Corporation. Invention is credited to Roger M. Bowley, Barry L. W. Chapman, Peter Mansfield, Robert Turner.
United States Patent |
4,978,920 |
Mansfield , et al. |
December 18, 1990 |
**Please see images for:
( Certificate of Correction ) ** |
Magnetic field screens
Abstract
The screen is provided by surrounding the coil producing the
magnetic field with a set of electrical conductors the currents
within the conductors being controlled in such a manner that the
field is neutrailized in a specific region of space, the current
distribution within the conductors being determined by calculating
the current within a hypothetical superconductive shield which
would have the effect of neutrailizing the field, the current
through the conductors thereby being a substitute for the
superconductive shield.
Inventors: |
Mansfield; Peter (Nottingham,
GB2), Chapman; Barry L. W. (Nottingham,
GB2), Turner; Robert (Nottingham, GB2),
Bowley; Roger M. (Nottingham, GB2) |
Assignee: |
National Research Development
Corporation (London, GB2)
|
Family
ID: |
27262794 |
Appl.
No.: |
07/338,392 |
Filed: |
April 14, 1989 |
Related U.S. Patent Documents
|
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
|
909292 |
Sep 19, 1986 |
|
|
|
|
Foreign Application Priority Data
|
|
|
|
|
Sep 20, 1985 [GB] |
|
|
8523326 |
Feb 6, 1986 [GB] |
|
|
8602911 |
Jun 19, 1986 [GB] |
|
|
8614912 |
|
Current U.S.
Class: |
324/318;
335/216 |
Current CPC
Class: |
H01F
27/36 (20130101); G01R 33/421 (20130101); H05K
9/00 (20130101) |
Current International
Class: |
H01F
27/34 (20060101); G01R 33/28 (20060101); G01R
33/421 (20060101); H01F 27/36 (20060101); H05K
9/00 (20060101); G01R 033/20 () |
Field of
Search: |
;324/300,307,309,318,322
;335/299,301,304 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Tokar; Michael J.
Attorney, Agent or Firm: Cushman, Darby & Cushman
Parent Case Text
This is a continuation of application Ser. No. 909,292, filed Sept.
19, 1986, which was abandoned upon the filing hereof.
Claims
We claim:
1. A screen for forming a protective barrier against a magnetic
field of a type which has been produced by an energized primary
electrical coil, said screen comprising:
a set of electrical conductors defining two sides, one of which
facing said primary electrical coil, and the other opposite said
one side and on an opposite side of the primary electrical coil;
and
means for supplying the conductors of the set with electrical
currents of magnitude such that a resultant distribution of said
currents differs from a primary current distribution in the primary
electrical coil and approximates an induced current distribution
which would be formed in a continuous superconductive surface
positioned in the place of said set so as to make the field
everywhere on said one side of the screen away from the primary
electrical coil substantially zero and thereby, when activated, to
completely reflect the magnetic field.
2. A screen as claimed in claim 1 in which the screen current
distribution localized to the surface of the hypothetical
superconducting sheet is determined by the deconvolution of the
magnetic field response function of the unit line elements of the
conductor currents with the field to be screened.
3. A screen as claimed in claim 1 in which the conductors of the
set are regularly spaced apart from each other.
4. A screen as claimed in claim 1 in which the conductors of the
set are connected electrically in parallel and have different
values of resistance in order to produce the desired screen current
distribution.
5. A screen as claimed in claim 4 in which the different values of
resistance of the set of conductors are produced by different
thickness of the respective conductors.
6. A screen as claimed in claim 4 in which the different values of
resistance of the set of conductors are produced by constructing
the conductors with different compositions having appropriate
values of electrical resistivity.
7. A screen as claimed in claim 1 in which the conductors of the
set carry equal currents but are spaced apart from each other by
different spacings in such a manner that the current in one
conductor is equal to an integrated incremental superconductive
surface current distribution, such incremental values being equal
for each conductor so as to produce the desired screen current
distribution.
8. A screen as claimed in claim 7 in which the number of screen
conductors is even.
9. A screen as claimed in claim 7 in which the number of screen
conductors is odd.
10. A screen as claimed in claim 1 in which the screen surface
current distribution Jy, for an infinite flat screen, screening an
infinite straight line primary, is defined by ##EQU56##
11. A screen as claimed in claim 1 in which the primary magnetic
field is created by a current F in the primary coil and in which
the current f defines the current in the screen and in which the
Fourier transforms of the current components of f are defined in
the case of coaxial cylindrical primary and screen geometry as:
##EQU57## and wherein the quantities F.sub.z.sup.m (k)
F.sub..phi..sup.m (k) being the components of the Fourier transform
of F are defined in an analogous way.
12. A screen as claimed in claim 11 in which the relationship for
the Fourier components of the currents induced in the screen to
those in the gradient coils are as defined as ##EQU58##
13. A screen for forming a protective barrier against a magnetic
field of a type which has been created by an energized primary coil
in which the primary coil is surrounded by two or more active
magnetic screening coils through which current is passed,
comprising: an inner screen and an outer screen, the inner screen
lying between the primary and the outer screen, each respective
screen comprising a set of electrical
conductors; and means for supplying the conductors of the set with
electrical currents of magnitude such that there is no appreciable
magnetic field outside the outer screen and the field within the
inner screen substantially corresponds to the field that could be
provided by the primary coil if the screen were not present.
14. A screen for forming a protective barrier against a magnetic
field of a type which has been created by an energized primary coil
in which the primary coil is surrounded by two or more active
magnetic screening coils through which current is passed
comprising: an inner screen and an outer screen, the inner screen
being coincident with the primary coil, each respective screen
comprising a set of electrical conductors; and means for supplying
the conductors of the set with electrical currents of magnitudes
such that there is no appreciate magnetic field outside the inner
screen and the field within the inner screen substantially
corresponds to the field that would be provided by the primary coil
if the screens were not present.
15. A screen as claimed in claim 13 in which the surface currents,
f.sub..phi..sup.l,m (z), f.sub..phi..sup.z,m (z) which lie on
hypothetical cylinders of radii b & o respectively
corresponding to the outer and inner screen, are defined in Fourier
space as ##EQU59##
16. A screen as claimed in claim 14 in which the surface currents,
f.sub.100 .sup.l,m (z), f.sub..phi..sup.z,m (z) which lie on
hypothetical cylinders of radii b & o respectively
corresponding to the outer and inner screen, are defined in Fourier
space as ##EQU60##
17. An actively magnetically screened coil set around the screen of
which is a second unscreened coil such that the mutual inductance
between the said set and second coil is zero, which total coil
system is supplied with currents at rf frequencies as an NMR
transmitter/receiver orthogonal coil system in which each coil may
be independently tuned to a different frequency.
18. A screen for forming a protective barrier against a magnetic
field of a type which has been produced by an energized primary
electrical coil, said screen comprising a set of electrical
conductors; and means for supplying the conductors of the set with
electrical currents of magnitude such that the resultant screen
current distribution is different from the primary current
distribution in the primary electrical coil and approximates the
induced current distribution which would be formed in a continuous
superconductive surface positioned in the place of said set so as
to make selected components of the field on the side of the screen
away from the primary electrical coil substantially zero and
thereby to act as a complete reflector of the selected components
of the magnetic field produced by the primary coil.
19. A screen for forming a protective barrier against a magnetic
field of a type which has been produced by an energized primary
electrical coil, said screen comprising: a first screen having a
first set of electrical conductors and a second screen having a
second set of electrical conductors, the first set of electrical
conductors being located spaced from the primary electrical coil,
and the second screen set of electrical conductors being positioned
intermediate between said first screen set and said primary coil;
and means for supplying the conductors of the first and second
screen sets with electrical currents of magnitude such that the
resultant current distribution is different from the current
distribution in the primary electrical coil and approximates the
induced current distribution which would be formed in continuous
superconductive surfaces positioned in the place of said screen
sets so as to make the field on the far side of the first screen
set away from the primary electrical coil substantially zero and
thereby to act as a complete reflector of the magnetic field
produced by both the primary electrical coil and the second screen
set of electrical conductors, and so as to make the field on the
primary coil side of the second screen set substantially equal to
the magnetic field of the primary in the absence of the screens the
second set thereby appearing as (a) a reflector of the field
produced by the final screen set and (b) transparent to the field
produced by the primary coil.
20. A coil set for producing a desired magnetic field within a
defined volume, said coil set comprising:
a first coil situated at a first location which defines the volume
and at least one second coil situated at a second location, which
embraces the volume,
the first coil having a first predetermined number of conductors to
produce a first current distribution within the first coil to
produce a first magnetic field, said at least one second coil
having a second predetermined number and pattern of conductors to
produce a second current distribution within the second coil to
produce a second magnetic field, and
wherein the second magnetic field produced by the second coil
provides a screen for the rest magnetic field produced by the first
coil such that the resultant magnetic field on the opposite side of
the second coil to the first coil is substantially zero, and the
resultant magnetic field on the opposite side of the first coil to
the second coil constitutes the desired magnetic field, and in
which the first and second predetermined number of conductors are
different from each other and in which the first current
distribution is different from the second current distribution.
21. A method of producing a desired magnetic field within a defined
volume, said method comprising the steps of:
situating a first coil at a first location which defines the volume
the first coil having a first predetermined number and pattern of
conductors designed to produce a first current distribution in the
first coil to produce a first magnetic field, and
situating at least one second coil at a second location which
embraces the volume, the second coil having a second predetermined
number and pattern of conductors designed to produce a second
current distribution in the second coil to produce a second
magnetic field,
wherein the second magnetic field produced by the second coil
provides a screen for the first magnetic field produced by the
first coil such that the resultant magnetic field on the opposite
side of the second coil to the first coil is substantially zero,
and the resultant magnetic field on the opposite aide of the first
coil to the second coil constitutes the desired magnetic field, and
in which the first and second predetermined number of conductors
are different to each other and in which the first current
distribution is different from the second current distribution.
22. A gradient coil system for use in an NMR apparatus including a
coil set for producing a desired gradient magnetic field within a
defined volume, the coil set comprising:
a primary coil designed to provide a gradient field situated at a
first location defining the volume and at least one screen coil
surrounding the main coil,
the primary coil having a first predetermined number and pattern of
conductors comprising a first set to produce when energized a first
current distribution in the primary coil to produce a screening
magnetic field, and
wherein the said screening magnetic field produced by the screen
coil provides a screen for the gradient magnetic field produced by
the primary coil such that the resultant magnetic field on the
opposite side of the screening coil to the primary coil is
substantially zero, and the resultant magnetic field in the defined
volume is the desired gradient magnetic field, and
in which the first and second predetermined number of conductors
are different from each other and in which the first current
distribution is different to the second current distribution.
23. A coil set for producing a desired magnetic field within a
defined volume, said coil set comprising:
a first coil situated at a first location which defines said volume
and at least one second coil situated at a second location which
surrounds said volume,
the first coil having a first predetermined number and pattern of
conductors to produce when energized a first current distribution
within the first coil to produce a first magnetic field,
the second coil having a second predetermined number and pattern of
conductors to produce when energized a second current distribution
within the second coil to produce a second magnetic field, and
wherein the second coil provides a screen for specified components
of the first magnetic field produced by the first coil such that
the specified components of the magnetic field on the opposite side
of the second coil to the first coil are substantially zero, and
the resultant magnetic field on the opposite side of the first coil
to the second coil constitutes the desired magnetic field, and
in which the first and second predetermined number of conductors
are different to each other and in which the first current
distribution is different to the second current distribution.
24. A coil set for producing a desired magnetic field within a
defined volume, said coil set comprising:
a first coil situated at a first location a second coil situated at
a second location,
the first coil having a first predetermined number and pattern of
conductors to produce when energized a first current distribution
within the first coil to produce the desired magnetic field and the
second coil having a second predetermined number and pattern of
conductors to produce a second current distribution in the second
coil to produce when energized a first screening magnetic
field,
the first and second predetermined number of conductors being
unequal and in which the first current distribution is not
identical to the second current distribution,
a third coil positioned intermediate between the first and second
coils,
the third coil comprising a third winding having a third
predetermined number and pattern of conductive to produce when
energized a third current distribution in the coil to produce a
second screening magnetic field, and
wherein the first and second screening magnetic fields combine
together with the field produced by the first coil to provide
substantially zero magnetic field outside the second coil without
causing any substantial change in the desired magnetic field in the
defined volume.
25. A screen for a magnetic field comprising;
a set of spaced electrical conductors; and
means for supplying electrical currents to the electrical
conductors;
said spaced electrical conductors having such a spacing, and said
supplying means forming such a current flow therein, as to satisfy,
and act to form, boundary conditions mimicking conditions which
would exist in a superconducting surface occupying a position of
said electrical conductors.
26. A screen as in claim 25, wherein said spaced conductors are
spaced at such discrete intervals, and have such a current flow, as
to cause integrals of surface current distribution between said
conductors at said intervals to be equal to one another.
27. A screen as in claim 25, wherein said conductors are disposed
in a plane and so spaced from one another, and so energized with a
current I.sub.n in a way such that : ##EQU61## wherein A is a
constant value, and ##EQU62## wherein I is the current I.sub.n in
the conductor, d is a distance from a point emanating the magnetic
fields to said plane, and r is a radial distance from the point to
the conductor.
28. A screen as in claim 27, wherein each said conductor carries an
equal current I, and wherein said conductors are located at
positions y1, y2, . . . yn, such that ##EQU63## where yx and yx1
are any two adjacent conductors y1, y2 . . . yn.
29. A screen as in claim 27, wherein each said conductor carries a
different current I.sub.n, and said conductors are equally spaced
from one another by a distance .DELTA.y, such that ##EQU64## where
.DELTA.y is a distance between the two conductors.
30. A screen as in claim 27, wherein said set of spaced electrical
conductor comprises two parallel screens, each having a current
distribution J1(d1) and J1(d2) following the equation ##EQU65##
wherein J.sub.n (d.sub.n) are induced surface currents induced from
the other screen.
31. A screen as in claim 25 wherein said magnetic field is produced
by a hoop having a radius r.sub.1, within which a current I.sub.1
flows, and said electrical conductors are located according to the
equation ##EQU66## wherein A is a constant, and ##EQU67## wherein
I.sub.2 is the current in the conductor, d is a distance from a
point emanating the magnetic fields to a plane in which the
conductor set is formed, and r is a radial distance from the point
to the conductor;
wherein a current flowing through the screen is ##EQU68## where
r.sub.1 is the primary coil radius and r.sub.2 is the screen
radius.
32. A screen for a magnetic field comprising;
a set of spaced, parallel, substantially straight, electrical
conductors forming a plane; and
means for supplying electrical currents to the electrical
conductors in a way such that the spacing of said spaced electrical
conductors and the currents therein satisfy and act to form
boundary conditions mimicking conditions which would exist in a
surface of a (hypothetical) superconducting plate occupying a
position of said electrical conductors.
33. A screen as in claim 32, wherein said spaced conductors are
spaced at such discrete intervals, and have such a current flow, as
to cause integrals of surface current distribution between said
conductors at said intervals to be equal to one another.
34. A screen as in claim 32, wherein said conductors are disposed
in a plane and so spaced from one another, and so energized with a
current I.sub.n, in a way such that: ##EQU69## wherein A is a
constant value, and ##EQU70## wherein I is the constant I.sub.n in
the conductor, d is a distance from a point emanating the magnetic
fields to said plane, and r is a radial distance from the point to
the conductor.
35. A screen as in claim 34, wherein each said conductor carries an
equal current I, and wherein said conductors are located at
positions y1, y2, . . . yn, such that ##EQU71## where yx and yx1
are any two adjacent conductor y1, y2 . . . yn.
36. A screen as in claim 34, wherein each said conductor carries a
different current I.sub.n, and said conductors are equally spaced
from one another by a distance y, such that ##EQU72## where y is a
distance between the two conductors.
37. A screen as in claim 34, wherein said set of spaced electrical
conductor comprises two parallel screens, each having a current
distribution J1(d1) and J1(d2) following the equation ##EQU73##
wherein J.sub.n (d.sub.n) are induced surface currents induced from
the other screen.
Description
FIELD OF THE INVENTION
This invention relates to magnetic field screens and has
application in NMR imaging apparatus.
BACKGROUND OF THE INVENTION
Current carrying magnet coils are used for a variety of purposes in
NMR imaging apparatus. Examples include large electro-magnets
designed to provide static magnetic fields to polarize nuclear
spins, magnetic field gradient coils which superimpose gradients
onto the static polarizing field and rf transmitter and receiver
coils.
In many cases the design of a magnet coil is such as to optimize
the magnetic field within a desired volume. However the coil
inevitably produces an extraneous magnetic field outside that
volume, especially relatively close to the coil. In the case of
large bore static electromagnets the high fields they generate will
produce undesirably strong extraneous fields at distances outside
the magnet corresponding to many magnet diameters. Such magnet
systems therefore require much free and unusable space around their
installation. Stray magnetic fields may be intolerable in hospitals
because of iron structures positioned around the installation site
which vitiate the homogeneity of the magnetic field. Additionally,
electronic equipment may not perform well in an environment which
has an extraneous magnetic field.
Furthermore, most NMR imaging systems utilize rapidly switched
magnetic field gradients in their operation. A major problem
epecially where super-conductive magnets are used, is the
interaction of the gradient field with the magnet itself. Existing
attempts to minimize this interaction include the use of conducting
metal screening sleeves. However, induced currents in these sleeves
or in the heat shield of the magnet decay with uncontrolled
relaxation times which make it difficult or even impossible to
implement some of the faster and more efficient NMR imaging
methods. This is because the decaying current produces image fields
superimposed on the desired gradient field. This uncontrolled time
dependence introduces phase artefacts which can completely ruin the
image.
In order to provide adequate access for patients, and to improve
gradient uniformity, it is desirable to maximize the diameter of
the magnetic field gradient coils in an NMR imaging machine.
However, this often causes the coils to be close to other
conductors, either the surfaces of cryogenic vessels (in
superconducting magnet systems), electromagnetic coil supports (in
resistive magnet systems), or ferromagnetic pole pieces (in
ferromagnetic systems). When gradients are switched rapidly, as
with many imaging techniques, eddy currents are induced in these
conductors which then contribute additional field gradients varying
in time and potentially very non-uniform in space. Typical time
constants for the decay of the eddy currents vary from a few
milliseconds to hundreds of milliseconds, depending on the type of
main magnet and the specific coil configuration.
The commonest solution to this problem is to tailor the input
applied to the amplifiers generating the gradient coil currents in
such a way that the gradient fields themselves follow the
prescribed time variation. The input voltage and gradient coil
currents are characteristically over-driven for the initial part of
the on-period of the gradient. But this remedy has a major
disadvantage. If the gradient coils are placed close to the coupled
surfaces, so that the eddy current field gradients may have the
same uniformity as the desired gradient, the gradient coils become
very inefficient and a large over capacity in the gradient current
amplifiers is required, since the `reflected` fields will be large
and in the opposite sense from the desired fields. If, on the other
hand, the gradient coils are reduced in size, to avoid the
amplifier capacity problem, then the reflected gradient fields will
in general be non-linear over the region of interest. Furthermore,
in either case there are likely to be reflected fields from more
distant conductors in the main magnet structure, each with its
distinct time constant and spatial variation.
The only effective solution is in some way to reduce the gradient
fields to zero at a finite radius outside be coupled to them.
Partially effective methods for magnetic screening in specific coil
geometries have been proposed hitherto in particular U.S. Pat. Nos.
3,466,499 and 3,671,902. These geometries are not generally useful
in NMR and NMR imaging.
SUMMARY OF THE INVENTION
It is an object of the invention to provide more efficient and
effective magnetic field screens for coil geometries useful in NMR
and NMR imaging.
It is a further object of the invention to provide efficient
magnetic field screens for any coil design.
It is a still further object of the present invention to provide
magnetic field screens for any desired component or components of a
magnetic field.
According to the invention a screen for a magnetic field comprising
a set of electrical conductors and means for supplying the
conductors of the set with electrical currents of magnitude such
that (a) the resultant current distribution approximates to the
induced current distribution in a hypothetical continuous
superconductive metal surface positioned in the place of said set
so as to appear as a complete reflector of magnetic field, and (b)
the resultant current distribution in this or other screens behaves
alone or in a combination with said other screens in such a way as
to appear to selectively reflect and/or transmit desired components
of magnetic fields of specific configuration through said screen or
screens.
Preferably the current distribution localized to the surface of a
hypothetical conducting sheet or sheets is determined by the
deconvolution of the magnetic field response function of the unit
line elements of that current with the field to be screened; such
problems being most conveniently solved in reciprocal space, which
is defined by those co-ordinates conjugate to real space used in
appropriate integral transform.
More preferably the problems are solved in Fourier space which is a
particular example of reciprocal space.
The present invention also provides a method of designing a
screening coil for selectively screening the field of a magnetic
coil.
The present invention further provides a gradient coil system for
use in NMR apparatus including a main coil designed to provide a
gradient field and a screen coil surrounding the main coil.
In one preferred arrangement the conductors of the set are
regularly spaced apart from each other. They may be connected
electrically in parallel and have different values of resistance in
order to produce the desired current distribution. In embodiments
of the invention the different values of resistance of the
conductors may be produced by different thicknesses of the
respective conductors or constructing them with different
compositions having appropriate values of electrical
resistivity.
In alternative preferred arrangements the conductors of the set
carry equal currents but are spaced apart from each other by
different spacings so as to produce the desired current
distribution.
It is a further object of the present invention to reduce acoustic
vibration in MR gradient coils by using the active screening
hereinbefore described.
In examples of carrying out the above invention a set of conductors
are arranged on a cylindrical former and with appropriate spacing
can be fed with equal currents. The spacing of the conductors of
the set and the magnitude of the currents are calculated using the
currents induced in a flat superconductive screen as the starting
point.
Additionally according to this invention the theoretical current
distribution in a continuous superconductive cylindrical shield
positioned in the place of the aforementioned set of electrical
conductors is calculated. Such a calculation enables an improved
screen to be provided, especially where a cylindrical screen is
required.
The calculations described herein represents an analytical
formulation of the problem, enabling a fully general calculation of
the current density in a cylinder required to cancel outside the
cylinder the magnetic fields generated by coils inside. The results
obtained are firstly applied to passive shielding, using a thick
high-conductivity or superconductive cylindrical tube to solve the
reflected fields problem without sacrificing gradient uniformity.
The conclusions arrived at can then be applied to active shielding;
the calculated current densities within the skin depth of a thick
cylinder or in a superconducting cylinder are mimicked using a
suitable arrangement of a set of wires supplied with currents of
appropriate magnitude.
For passive shielding using a normal conducting cylinder to be
effective, the skin depth .sigma. in the shield at the lowest
frequency represented in the particular gradient switching sequence
must be much smaller than the thickness d of the wall of the
cylinder. For an echo planar switched gradient, for instance, with
a fundamental frequency of 1 KHz, this entails a wall thickness of
.about.10 mm of aluminium. For switched gradients such as that used
for slice selection, where there is a non-zero d.c. component of
the fields at the cylinder surface, passive shielding is not
appropriate.
When the criterion of .sigma./d<<1 is met, the time
dependence of reflected fields will be identical to that of the
applied field, and it is only the spatial nonuniformity of the net
magnetic field which is of concern. Analytic calculation of the
ensuing fields enables the necessary corrections to coil spacings
to be made.
By Lenz's law, a magnetic field screen constructed in accordance
with the above design criteria produces a magnetic field which
opposes the field generated by the primary magnetic coil that it is
designed to screen. For a given current in the primary coil the
resultant magnetic field generated within the volume embraced by
the coil is reduced and its spatial variation is also changed by
the presence of the screen currents thus introducing undesirable
variations in the primary field.
It is therefore a further object of the invention to provide a
screening coil arrangement in which the above disadvantages are
overcome.
Accordingly the present invention also provides a magnetic coil
surrounded by two active magnetic screening coils, namely an inner
screen and an outer screen, each respective screen comprising a set
of electrical conductors and means for supplying the conductors of
the set with electrical currents of magnitudes such that there is
no appreciable magnetic field outside the outer screen and the
field within the inner screen substantially corresponds to the
field that would be provided by the said magnetic coil if the
screens were not present.
BRIEF DESCRIPTION OF THE DRAWING
In order that the invention may be more fully understood reference
will now be made to the accompanying drawings in which:
FIGS. 1 to 10 are explanatory of the underlying theory;
FIGS. 11, 12, 13, 14, 15, 16a, 16b, 17a, and 17b illustrate in
diagrammatic form various embodiments of the invention;
FIG. 18 shows a cylindrical co-ordinate system used in calculating
the magnetic fields produced by current flow on a cylindrical
surface;
FIG. 19 illustrates saddle-shaped coils used as magnetic gradient
field coils;
FIG. 20 illustrates the configuration of one octant of a set of
screening coils in accordance with the calculations described
herein;
FIG. 21 shows curves for optimizing the positions of the arcs of
the saddle coils of FIG. 19;
FIG. 22 illustrates diagrammatically the magnetic field produced by
an unscreened primary coil in the form of a single hoop;
FIG. 23 illustrates the same hoop with a double screen embodying
the invention;
FIG. 24 is a graph showing the magnetic field at different radial
positions that is produced by the FIG. 23 arrangement;
FIG. 25 is a perspective view of a double saddle coil used to
produce transverse gradient fields which is screened by a double
screen embodying the invention;
FIGS. 26 to 33 illustrate ways of providing varying current
distribution over a desired area;
FIG. 34 shows a parallel band arrangement;
FIG. 35 shows a series arrangement;
FIG. 36 shows various arrangements for assisting in reduction of
acoustic vibration in MR coils by a gradient wire with (a) a wire
pair (b) a wire array (c) a pair of conducting plates used to
nullify the main field in the neighbourhood of the gradient coil
and (d) a double active screen arrangement;
FIG. 37 shows winding strategies for screening wires about gradient
coils of the (a) standard circular design and (b) saddle design;
and
FIG. 38 illustrates the screening of one coil from the magnetic
field of another.
DETAILED DESCRIPTION OF THE INVENTION
The basic theory and ideas are developed from the simple case of an
infinite straight wire parallel to an infinite flat conducting
sheet. FIG. 1 shows a long straight wire carrying a current I. The
magnetic field B.sub.o at a point P which is at a distance r normal
to the wire is given by ##EQU1## If the current is changing with
angular frequency .omega. and the wire is near to an infinite
conducting sheet as shown in FIG. 2 (also if the current is static
and the sheet is superconducting), the magnetic field undergoes
distortion at the metal surface. Let us assume no field penetration
into the screen, i.e. the angular frequency .omega. and the metal
conductivity .sigma. are sufficiently high, then the boundary
conditions for the magnetic field at the surface are ##EQU2## The
details of the field at a point P due to a wire at a distance d
from the sheet may be conveniently calculated as shown in FIG. 3
using the method of images which assumes a wire at a distance d
from the other side of the sheet carrying a current -I.
In general, current in the sheet surface is directly related to the
tangential field H.sub.y. The total field B.sub.o at P, FIG. 4, is
given by Equation (1) and may be resolved into components B.sub.x
and B.sub.y in the x and y directions respectively ##EQU3## Taking
the image current -I into account, FIG. 5, we obtain the total y
direction field B.sub.TOT at point P for a current I at point 0 and
its image current -I at a point 0'. ##EQU4## We also note from FIG.
5 that
and
If P is on the conducting sheet surface r=r' in which case, see
FIG. 6. ##EQU5## From Equations (9) and (10) we obtain ##EQU6##
Consider now the line integral of the magnetic field in and close
to the metal surface, FIG. 7. By Ampere's theorem we have ##EQU7##
where J.sub.y is the surface current density and ds an area element
and dl a path element. For a short path l parallel to the surface
H.sub.y is constant. The line integral is therefore
But in the metal H.sub.y '=0 and H.sub.x =H.sub.x ' yielding for
dl.fwdarw.0
The surface current distribution is therefore ##EQU8## This
function is plotted in FIG. 8.
To determine the field produced by the surface current density
distribution, let us assume we have a surface distribution J.sub.y
within a flat metal sheet as in Equation (15). Consider an element
of surface dl with current .sigma.i, FIG. 9. This current is given
by ##EQU9## The elemental field at point P which is a distance r
from the element and distance d from the sheet is ##EQU10## The
tangential component of which is: ##EQU11## The total field is
##EQU12## which yields ##EQU13## Thus the field at point P distance
d from the surface current distribution is equivalent to a mirror
current of -I at distance 2d from P.
The total surface current ##EQU14##
The results derived above suggest that instead of using a metal
plate to screen alternating fields, an active screen comprising a
mesh of wires may be used in which a current pattern is externally
generating to mimic a desired surface distribution. This situation
is shown in FIG. 10. Wires at positions y.sub.1, y.sub.2 . . .
y.sub.n in the y direction all carrying an equal current I are
spaced at different discrete intervals corresponding to equal areas
A under the J.sub.i curve of FIG. 8. For equal currents in the
wires, the wires must be unequally spaced with positons y.sub.n
which satisfy the relationship ##EQU15## for an even array of 2N
wires spread about the y origin. For an odd array of 2N+1 wires
with one wire at the origin we have ##EQU16## where n =1, 2, 3 . .
.
Alternatively, wires may be equally spaced with different currents
chosen such that ##EQU17## In either case, since we have arranged
to satisfy the original boundary conditions on the surface of a
fictitious plate, the magnetic field in the half plane (x,.+-.y)
approaches zero. The degree of screening depends ultimately on the
number of wires used in the active screening mesh. An example of
such an active screen is shown in FIG. 11 for a distribution of
current carrying conductors corresponding to FIG. 10 all carrying
an equal current I. The field B on the opposite side of the screen
is effectively zero.
If two parallel screens are used, each will have primary current
distributions of J.sub.1 (d.sub.1) and J.sub.1 (d.sub.2) given by
Equation (15). This is shown in FIG. 12. However, each induced
current distribution will induce further changes in the
distribution in the opposite plate represented by additional terms
J.sub.n (d.sub.n). This is equivalent to a set of multiple
reflections, FIG. 13, which correspond to an infinite set of
images. When d.sub.1 =d.sub.2 =d, image currents occur at
x=.+-.2nd, n=1, 2 . . . The total induced surface current in each
sheet is the sum of ##EQU18##
The boundary conditions at the metal surface ensure that the normal
laws of reflection apply. However, when active current screens are
used, the reflection laws may be selectively changed to reflect any
images using the J.sub.n (d)'s corresponding to particular
distances d.
An example of a gradient active screen is shown in FIG. 14 for a
single circular hoop of diameter 2a. Let this be screened by an
active current mesh in the form of a cylinder of radius a+d. In a
metal cylinder, image
hoops appear at radii r=b+d, 3b.+-.d, 5b.+-.d, etc. However, since
the effect of these distant images diminishes quite rapidly, it is
reasonable to approximate a screen with J.sub.1 (d) corresponding
to the plane sheet case, Equation (15). Better approximations may
be obtained by an iterative numerical approach. Although exact
solutions for the surface current in a cylinder exist, when actual
wire screens are constructed, the numerical approach is preferred
since it automatically takes account of the finite number of wires
and their discrete spacing. The screen current is ##EQU19## where
N.sub.2 is the number of screen wires in the mesh of radius r.sub.2
each carrying a current I.sub.2 and N.sub.1 is the number of turns
in the primary coil radius r.sub.1 carrying a current I.sub.1. The
factor .alpha. is of the order of unity and is chosen to optimize
the screening. The whole optimization procedure is accomplished by
a computational process which generalizes to applying minimization
of the total field over a limited region of space. Mathematically
this is conveniently achieved by a least squares method. For
practical ease, it is desirable to have both coil and screen driven
from the same current source. Since the total screen current is
less than the primary current it will in general be necessary to
take parallel combinations of the screen mesh so that the total
system may be driven in series. However, a parallel arrangement is
also possible in which the screen wires are varied in resistance
and/or impedance in such a way that when driven from a voltage
source appropriate currents flow. Because of the screening effect
the inductance of both versions of the coil system should be
low.
Sets of screened hoops may be used to construct screened magnets
producing uniform magnetic fields. The presence of the screen
around one hoop is approximately equivalent to an image hoop with
negative current producing an opposing field. For a Helmholtz coil
pair the intercoil spacing equals the coil radius a. When screened,
however, the spacing must be changed so as to make the second
derivative of the field B.sub.z with respect to z vanish for the
combined coil system. Similarly for a Maxwell pair designed to
produce a linear magnetic field gradient, the intercoil spacing is
ideally a .sqroot.3. This is shown in FIG. 15. The two hoops
forming a Maxwell pair are screened by a concentric pair of
screening meshes offset axially from each other. The combined
screen current distribution is also shown. Again, however, when
screened coils are used, a new spacing obtains which makes the
third derivative of B.sub.z with respect to z vanish for the total
coil system. The process of optimization of coil geometry can be
done analytically for simple coil structures as discussed above.
For more complicated systems such as screened saddle geometry
gradient coils, it is preferable simply to find by computational
means the position where the chosen derivative vanishes, or is
minimized.
For NMR imaging sytems using superconducting magnet coils it is
convenient to use saddle coils to produce the transverse gradients
##EQU20## In some imaging techniques, at least one of the gradients
can be very large making interaction with the main magnet
potentially serious. FIG. 16 shows one half of a G.sub.x screened
gradient coil system. A screened single saddle coil is shown in end
view at (a) and plan view at (b). The dotted lines correspond to
the screening mesh. To a first approximation, the screen current
profile is J.sub.1 (d). Better screening may be obtained by an
iterative procedure which minimizes the field outside the
screen.
FIG. 17 shows a screened rectangular G.sub.x gradient coil set with
1/2 screen. Again, if a d<<2a, J.sub.1 (d) may be used as a
good approximation for the screen current distribution. For better
results other reflections can be included or the iterative
procedure used to minimize fields outside the coil.
NMR imaging systems require rf coil systems to deliver rf pulses to
the specimen and to receive signals induced in the sample. Because
of the number of other coil systems required for field gradients,
there is always a problem of space. With normal rf coil
arrangements the field outside the coil drops off rather slowly. In
order to minimize coil interactions which can lower the Q value, rf
coil diameters are often chosen to be around 0.5 to 0.7 of the
gradient coil diameter. With shielded rf coil designs, it may be
possible to utilize more of the available space without loss of
performance.
A systematic procedure for reducing extraneous magnetic fields
outside the active volume of static magnets, field gradient coil
systems and rf coils has been described. In NMR imaging, reduction
of stray fields in all three types of coil structure is extremely
important. The method utilizes active magnetic screens and has the
advantage that such screens operate independently of frequency down
to dc. Some price is paid in terms of reduction of field in the
active volume compared with that of the free space value. With time
dependent gradients, the price is in general acceptable since for
fast NMR imaging schemes employing rapid gradient switching, active
coil screening may be the only way in which such imaging schemes
may be made to operate in the relatively close confines of an
electromagnet.
In what has previously been described, iterative and least squares
approximation methods are used to obtain actual screening wire
positions. It is possible to obtain these positions directly using
analytical methods. If the gradient coils and screens are located
on cylindrical formers, it is natural to use cylindrical
co-ordinates .rho., .phi., z in order to retain the symmetry of the
system. The z axis is taken to lie along the axis of the cylinder
as shown in FIG. 18.
The vector potential A, is used to describe the magnetic field.
This has the components A.sub..rho., A.sub..phi., A.sub.z given by
##EQU21## where J is the current density and dv' is a volume
element corresponding to the position vector r'. There is no
current flow in the radial direction in many problems of interest
so J has only z and .phi. components.
It has been assumed that currents induced in the shield are
confined to the surface of a cylinder of radius b. The gradient
coils to be shielded are mounted on a cylindrical former of radius
a which is coaxial with the shield. The currents can then be
written as
where F describes the current in the gradient coils, f describes
the current induced in the shield and .delta. is the Dirac delta
function. It is possible to derive relationships between F and f
from the condition that the radial component of the magnetic field
is zero on the surface of the shield. The other constraint which is
used is the equation of continuity, which, in the absence of charge
accumulation is
The vital step in the analytic treatment of this system is the use
of the Green's function expansion ##EQU22## where m is an integer
and .rho..sup.< (.rho..sup.>) is the lesser (greater) of
.rho. and .rho.', and I.sub.m (z) and K.sub.m (z) are modified
Bessel functions. To use equation (30) in equations (25), (26) and
(27) it is helpful to define a type of Fourier transform of f and F
as follows: ##EQU23## where the quantities F.sub.z.sup.m (k) and
F.sub..phi..sup.m (k) are defined in an analogous way. The
components of A thus become (e.g. for .rho.>b): ##EQU24##
Similar expressions can be obtained when .rho.<a or a
<.rho.<b.
Now let the boundary condition that the radial component of the
negative field B.rho.=0 at .rho.=b be applied. This is equivalent
to ##EQU25## Equations (33) and (34) are now used and terms varying
as e.sup.im.phi. are equated. This gives ##EQU26## This equation
can be simplified using the relations derived from the equations of
continuity, ##EQU27## for the currents in the shield, and ##EQU28##
for the currents in the gradient coils. These equations are
equivalent to ##EQU29## and ##EQU30## The recurrence relations for
Bessel functions are also used, from which can be derived the
identity ##EQU31## Here the prime denotes the derivative. Equations
(37), (40), (41) and (42) can be combined to obtain the elegant
expressions, ##EQU32##
These identities provide the means of calculating fields due to any
combination of currents constrained to flow on the surface of a
cylinder inside a conducting shield. This will now be illustrated
with an example.
For transverse field gradients it is common to use a saddle coil
configuration such as shown in FIG. 19. Two pairs of saddle coils
are shown. One pair extends between -d.sub.1 and -d.sub.2 along the
z axis. The other part extends between +d.sub.1 and +d.sub.2 along
the z axis. With energization of the coils as marked a gradient
field is produced in the form of a magnetic field along the z axis
which has a gradient in the x direction. The field produced by such
coils extends widely outside the cylinder on which the coils are
wound unless they are shielded by a conductive sleeve.
For the standard coil geometry with 120.degree. arcs for the saddle
coils. ##EQU33## where H(x) is the Heaviside step function. This
has the Fourier transform ##EQU34## This is zero for m even or an
integer multiple of 3. This leaves non-zero terms for m=1, 5, 7, 11
etc.
The position of the screening arcs can now be determined as
follows. First it is necessary to specify the continuous current
distribution to which the arcs approximate as set out in equations
(43) and (44).
The actual surface current density may then be written
##EQU35##
The next step is to determine the stagnation point of this current
density, that is, the point S=(O,d) at which F.sub..phi. and
f.sub.z are both zero, around which the surface current flows. By
symmetry this occurs at .phi.=0, and since f.sub.z (O, z)=0 for all
z, it may be found by solving f.sub..phi. (0, z)=0, by successive
approximation.
Having found S, the integrated surface current I.sub.t crossing the
line SP between S and an arbitrary point P on the cylinder (FIG.
20) is given by ##EQU36## (using the surface version of the
divergence theorem). Hence ##EQU37##
The contours of the induced surface current may now be found by
setting I.sub.t (.phi., z)=constant. These may be translated into
positions of screening arcs in the following way. The total current
in the cylinder I.sub.t (0, 0) is divided by 2N, where N is the
number of screening arcs required, and the M'th arc consists of the
contour where ##EQU38##
In practice I.sub.t (.phi., z) is calculated over a grid of
50.times.45 points, and the contours are found by linear
interpolation between the calculated points.
To check that these arcs indeed provide adequate screening of
saddle coil fringe fields, the total field can be calculated using
the Biot-Savart Law, taking as line elements d.sub.1 the intervals
between successive calculated co-ordinate pairs along each arc.
Given a set of saddle, coils with radius 0.31 m and arc spacings
from the center d.sub.1 and O.sub.2 of 0.108 m and 0.404 m, the
shielding produced at 0.55 m radius, using six screening arcs on a
cylinder of radius b=0.45 m, is as follows: ##EQU39## For
comparison, the maximum field at 0.55 m radius produced by an
unscreened small scale saddle coil set (a=0.16 m, d.sub.1 =0.56 m,
d.sub.2 =0.206 m) is 0.86.times.10.sup.-7 T/A-turn.
FIG. 20 shows the configuration of one octant of the set of
screening coils calculated above.
A larger number of screening arcs, or the use of foil rather than
wire conductors, will further reduce the fringe fields.
Screening a set of saddle coils, the spacing of which has been
optimized without the screen present, inevitably reduces the
uniformity of the gradients produced. The uniformity may be
recovered however by adjusting the arc spacing as follows:
The z component of the magnetic field can be derived from equations
(34), (35), and (44) to give ##EQU40## This becomes, with
substitution of equations (45) and (46) ##EQU41## It is now
possible to optimize the gradient linearity by adjusting the arc
positions of the saddle coils. The terms for m=5 are of fifth order
in x, y or z, whereas there are terms for m=1 which are of first
order in x and of third order in x, y and z.
The optimum choice of the parameters d.sub.1 and d.sub.2 is the one
which removes the third order terms. This gives the condition
##EQU42##
There are now two unknown quantities, D.sub.1 (=d.sub.1 /a) and
D.sub.2 (=d.sub.2 /a) and only one constraint, so it is not
possible to give a unique choice of parameters. However it can be
ensured that each parameter separately satisfies the equation
##EQU43## (with .alpha.=b/a) for this automatically satisfies
equation (54). Values of D.sub.1 and D.sub.2 as a function of
.alpha. are shown in FIG. 21.
It is possible to improve on this arrangement by altering D.sub.1
and D.sub.2 slightly (subject to the constraint given by equation
(55)) and minimizing the fifth order terms. The final choice of
values of D.sub.1 and D.sub.2 depend on whether the x or z
variation is considered to be more important. The values of D.sub.1
(.alpha.) and D.sub.2 (.alpha.) shown represent an excellent
starting point in the search for the optimum position of the saddle
coils.
Referring now to FIG. 22 there is shown therein a magnetic coil in
the form of a single wire hoop 1 of radius a carrying a current +I.
In FIG. 23 the same wire hoop 1 is surrounded by two active
magnetic screens S1 and S2. Each screen comprises a set of
electrical current carrying conductors but for simplicity the
screens are shown as sections of cylinders. Outer screen S1 is a
cylinder of radius b and inner screen S2 is a cylinder of radius
c.
With appropriate screen current density distributions screens S1
and S2 act together as a flux guide confining the field lines in
the manner indicated. The design criteria for the current density
distributions are set out below.
For a single conducting screen S, the boundary conditions of the
magnetic field B(r-r') at the surface of the screen require only
that the axial component B.sub.z (r-r', z'z') is considered which
for a coaxial hoop is independent of azimuthal angle .phi.. For
perfect screening it is required that
for r>b and for all z, where B.sub.z (r-a,z) is the primary hoop
field per unit current and B.sub.z.sup.s (r-b,z) is the total field
generated by the screen. The screen field is the convolution of the
surface current density j.sub..phi. (z) with the hoop magnetic
field response per unit current. Equation (56) may therefore be
written as ##EQU44## Note that ##EQU45## where q may be taken to be
k or z. The spatial Fourier transform of equation (57) gives
where k is the reciprocal space wave number.
Equation (58) may be generalized for two screens with current
densities j.sub..phi..sup.1 (k) and j.sub..phi..sup.2 (k) as set
out below. For zero field in the range r.gtoreq.b and the
unperturbed hoop field for r.ltoreq.c there is obtained
The current hoop fields are evaluated numerically along the z-axis
on the appropriate cylindrical surface using the Biot-Savart Law,
then Fourier transformed to k-space. This allows numerical solution
of the simultaneous equations (59) and (60) yielding the k-space
current densities. These are then inversely transformed to yield
the actual screen current density distributions.
In this example consider a primary hoop of radius a=0.5 m shielded
by two active screens S1, S2 with radii b=0.75 m and c=1.0 m
respectively. The hoop current is 1A. Using the computed
distributions, the total magnetic field generated by the screen
system in the hoop plane (z=0) is calculated as a function of r.
This is shown in FIG. 24 which is a graph of a calculated
z-component of magnetic field B.sub.z (r,0) against radius in the
plane of a doubly screened flat current hoop of dimensions as in
FIG. 23. The unscreened hoop field is shown by the broken curve and
is equal to B.sub.z for r<0.75 m. As expected for r<c, the
field B.sub.z exactly equals that of the unscreened hoop. For
r>b, the field B is zero. Between the screens, the field is
wholly negative. The total screen currents are given by I.sub.1
=j.sub..phi..sup.1 (0) and I.sub.2 =j.sub..phi..sup.2 (0). In this
case I.sub.2 =-I.sub.1 =0.57 I. The results have been produced by
numerical methods using a computer.
The inner screen S2 behaves like a complete absorber of the primary
field. However, once trapped between the screens, the field is
completely internally reflected by S1 and S2. The screen S2 behaves
like a perfect one-way mirror. Practical screens having these
properties clearly cannot be continuous metal surfaces. Externally
driven discrete wire arrays which approximate the calculated
continuous surface current densities are used instead. For a common
screen current, wires are placed at positions corresponding to
equal areas under the current density distribution integrated over
discrete intervals, as described in the above patent
specifications.
Although active screening of a single hoop has been described in
the above example, the principles of double screening apply to
other geometries, for example flat screens as well as more complex
coil geometries, some of which are used to produce linear gradients
in NMR imaging.
On the basis of the analytical expression for the component of the
magnetic field B.sub.z which is set out in equation (52), equations
(59) and (60) become, for k-space.
which yield the current densities ##EQU46## For k=0, K.sub.1
(kb)/K.sub.1 (kc)=c/b and I.sub.1 (ka)/I.sub.1 (kb)=a/b from which
it is deduced that the total currents I.sub.1, I.sub.2 flowing in
S1 and S2 are equal and opposite. From equations (63) and (64)
there is obtained ##EQU47## If a=c thereby making the primary coil
and S.sub.2 coincident, the condition b=a.sqroot.2 makes I.sub.1
=-I==I.sub.2 and means that the coil and screens may be placed in
series. For discrete wire arrays chosen to approximate the required
continuous current distributions, equations (65) and (66) become
##EQU48## where N.sub.o I.sub.o, N.sub.1 I.sub.1 and N.sub.2
I.sub.2 are the ampere-turns for the primary coil and screens S1
and S2 respectively. A more general series coil arrangement is
possible by varying both the turns and screen radii in equations
(67) and (68).
A Maxwell pair of two hoops with opposite currents may be used to
generate a z-gradient field. Since double screening produces the
free space field of hoops in the region r<a, the usual coil
spacing a.sqroot.3 obtains for the most linear gradient along the
z-axis.
FIG. 25 shows a simple saddle coil of radius a used to produce a
transverse gradient. Let this be shielded by two active cylindrical
screens S.sub.1 and S.sub.2 with radii b and c respectively where
a.ltoreq.c<b. For a standard saddle geometry with 120.degree.
arcs, the primary current is ##EQU49## where H(o) is the Heaviside
function. The Fourier transform of equation (69) is ##EQU50## This
is zero for m even or an integer of 3. Since there are now many
values of m, equations (61) and (62) are generalized to give for
two shields
From equations (71) and (72) there is obtained the results that
##EQU51## These results evaluated at k=0 give for each separate arc
pair at .+-.d.sub.1 and .+-.d.sub.2 the total azimuthal screen
currents I.sub.1 and I.sub.2. The dominant components of these
currents arise from the m=1 terms and may be simplified by noting
that at k=0, I.sub.1 '(ka)/I.sub.1 '(kb)=1 and K.sub.1
'(kb)/K.sub.1 '(kb)/K.sub.1 '(kc)=c.sup.2 /b.sup.2. The
z-components of current flowing in the screens may be calculated by
noting that ##EQU52## which expanded gives ##EQU53## Fourier
transforming equation (76) gives ##EQU54## Equation (77) for R=b or
c and equations (73) and (74) give on transforming to z-space the
actual screen surface densities.
The above results have shown that by introducing a second active
screen the spatial response within a primary coil can be made to be
independent of the surrounding screens. The inner screen may be
positioned to be coincident with the primary coil and still retain
the above advantages. While in the above description two active
magnetic screens have been employed it is possible to extend the
principles of active magnetic screening of coil structures to
multiple screens. Use of two or more than two screens has the
advantage that the screens can be designed so as not to vitiate or
change the character of the magnetic field spatial response from
the primary coil structure being screened. This is true even when
the inner screen of a two or multiple screen structure is
coincident with the primary coil structure.
The calculations and analytical expressions presented refer to
continuous current density distributions in the screens. Practical
active screens require discrete wire arrays which simulate the
continuous current density distributions. Discrete screens also
allow exploitation of the selective transmissive and reflective
properties of the active magnetic shields.
The object of a magnetic screen is to provide a spatial current
distribution which mimics that which is theoretically induced in a
real and/or fictitious continuous conducting sleeve around a coil
structure in which the coil itself is producing a time-dependent
magnetic field gradient. Equation 24 describes an arrangement in
which wires are equally spaced by with currents chosen again to
mimic the induced surface current distribution in a continuous
metal screen.
Several methods of varying the current in these conductors are:
1. To include in each conductor a small resistor chosen to give
required current.
2. To change the diameter or the shape of the wire so as to affect
its resistance in the right manner.
3. Change the composition of the conductor to affect its
resistance. These situations are covered in FIGS. 30 and 31.
It will also be clear from the above discussion that when the
conductor size is changed as in FIG. 31 and in the limit of
uninsulated touching wires, we have the situation shown in FIG. 27.
An alternative arrangement to this is a profiled cross-sectional
band of material as shown in FIG. 26. Alternative ways of producing
this band or its effect are shown in FIGS. 28 and 29. The thickness
t of the band must be chosen such that the electro magnetic
penetration depth .delta. is less than t for the highest frequency
present in the current switching waveform.
It will be seen that the above conductor arrangements 26 to 31
could be parallel arrangements or bands as in FIG. 34 fed with
appropriate total current along the edges indicated. However, it is
conceivable that one could manufacture multi turn band structures
producing a series arrangement as in FIG. 35.
An alternative approach using a constant standard wire section
employs the wire arrangements in FIGS. 32 and 33. Here the wires
are stacked in such a manner as to produce the desired current
distribution. If the wires are uninsulated and touching this is an
alternative method of producing the equivalent arrangement of FIG.
26. However, if the wires are insulated and touching it will
readily be seen that all the turns may be in series. A series
arrangement will have a much higher inductance but require only a
small common current through each turn. The parallel arrangements
discussed earlier require the driver circuitry to provide the total
field screen current for a one turn arrangement as in FIG. 34.
In order to obtain images by magnetic resonance it is necessary to
switch gradients rapidly. For typical magnetic gradient strengths
the current I required is commonly around 150 Amps. These currents,
when flowing in the static field B produce a force per unit length
of
on the wires carrying this current. For parts of the gradient coil
the field B and the current I may be perpendicular thus maximizing
this force. The resultant motion of the wires causes acoustic noise
which can be very loud if strongly coupled to the coil former. This
problem is growing in severity with the use of higher static
fields. The situation is further exacerbated by use of larger
gradient coils where the wire length is greater over which the
force can act. Rapid imaging strategies can also create more
noise.
Solutions to the noise problem such as embedding the wires in rigid
materials like concrete do help by lowering the natural resonances
of the coil former and by absorbing some acoustic energy.
Surrounding the wires with some soft acoustic absorbing material
such as cotton wall can also reduce the noise. But these approaches
treat the symptoms rather than the cause.
In a further example of the use of the present invention the
problem is solved at source by reducing the B field to zero in the
vicinity of the wires. This eliminates the force on and hence
motion of the wires. As well as solving the noise problem, the lack
of motion of the wires removes the possibility of progressive
fatiguing and fracture of the conductors.
In order to do this the wires on the gradient coil are locally
screened magnetically from B. This is achieved by using the
principles of active screening. A single screen arrangement is
created by arranging the screening wires in series. Different
arrangements are shown in FIG. 36. With these arrangements the far
field, i.e. coordinates x, z for a point P a distance R>> a
where a is the half separation of the screen pair (FIG. 36), is
effectively unperturbed. For an infinite straight wire screen the
interior and exterior screening fields B.sub.c and B.sub.p
(R>>a) are respectively ##EQU55## For small separation
B.sub.c can be very large and B.sub.p small. This represents a net
fall off rate which goes as 1/R.sup.2. For finite wires the fall
off is basically dipolar i.e. goes as 1/R.sup.3.
For parallel infinite sheets the fields are
where J is the current density per unit length. For the
arrangements sketched in FIGS. 36a to 36c respectively the
screening efficacy will lie between the cases covered in Equations
(78) and (79). Because the screen produces a static field,
perturbation of the main field can be eliminated with a shim set.
The screen or counter field generator need be active only during
the experimental period.
To further reduce the extraneous static fields produced by the wire
screening arrangement, a second active screen may be used in
addition to the first screen.
Such a double active screen arrangement is sketched in FIG. 36. The
wire W is a roughly screened by a parallel plate arrangement
S.sub.1. Residual far fields arising from non-cancellation outside
the plates is annulled by a second active screen S.sub.2 comprising
a set of conductors distributed appropriately. FIG. 37 shows two
local wire screening strategies for a circular hoop (37a) and a
saddle gradient (37b).
Using the wire screening arrangement described, the benefits of
rapid switching of large gradients may be obtained within a high
static magnetic field without acoustic noise.
Screening could also be applied to a Hall probe to increase its
sensitivity to small field variation by removing the main central
field.
In addition to the application of active magnetic screening to
electromagnet and gradient coil design there are a number of
possible applications in rf coil design. For example a fully
screened series wound rf coil placed coaxially inside an unscreened
coil would have zero mutual inductance. However an NMR sample
placed inside the screen coil would sense fields generated by both
coils. The coils though coaxial therefore behave electrically as
though they were orthogonal This can have advantages in
multi-nuclear irradiation and detection.
A schematic example of one such possible configuration is shown in
FIG. 38 where an inner coil C1 is wound inside an outer coil C2.
The inner coil C1 can be screened by providing a suitably wound
screening coil CS between the two coils C1 and C2. The screen coil
CS is as shown connected in series with coil C1 to pass the same
current. It is generally longer than the coils C1 and C2 to provide
efficient screening and is wound such that the current in coil CS
opposes that in coil C1. The exact positioning of the wires in coil
CS is determined by using the above approach
* * * * *